![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > df-ac | Unicode version |
Description: The expression
CHOICE will be used as a readable shorthand for any
form of the axiom of choice; all concrete forms are long, cryptic, have
dummy variables, or all three, making it useful to have a short name.
Similar to the Axiom of Choice (first form) of [Enderton] p. 49.
There are some decisions about how to write this definition especially around whether ax-setind 4538 is needed to show equivalence to other ways of stating choice, and about whether choice functions are available for nonempty sets or inhabited sets. (Contributed by Mario Carneiro, 22-Feb-2015.) |
Ref | Expression |
---|---|
df-ac |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wac 7206 |
. 2
![]() | |
2 | vf |
. . . . . . 7
![]() ![]() | |
3 | 2 | cv 1352 |
. . . . . 6
![]() ![]() |
4 | vx |
. . . . . . 7
![]() ![]() | |
5 | 4 | cv 1352 |
. . . . . 6
![]() ![]() |
6 | 3, 5 | wss 3131 |
. . . . 5
![]() ![]() ![]() ![]() |
7 | 5 | cdm 4628 |
. . . . . 6
![]() ![]() ![]() |
8 | 3, 7 | wfn 5213 |
. . . . 5
![]() ![]() ![]() ![]() ![]() |
9 | 6, 8 | wa 104 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
10 | 9, 2 | wex 1492 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
11 | 10, 4 | wal 1351 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
12 | 1, 11 | wb 105 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
This definition is referenced by: acfun 7208 |
Copyright terms: Public domain | W3C validator |